square metres per second (m2/s) to square feet per second (ft2/s) conversion

What is the square metre per second?

The square metre per second (m²/s) is the SI derived unit of kinematic viscosity and of diffusivity. Kinematic viscosity is the ratio of a fluid's dynamic viscosity to its density, describing how readily a fluid flows under gravity independent of its mass.

Definition

One square metre per second is the SI coherent unit of kinematic viscosity, obtained by dividing dynamic viscosity (Pa·s) by density (kg/m³):

$$1\ \text{m}^2/\text{s} = 1\ \text{m}^2/\text{s}$$

Equivalently, $1\ \text{m}^2/\text{s} = 1\ \text{Pa·s} \div 1\ \text{kg/m}^3$. Its dimensions are area per time (L²T⁻¹). The same unit measures mass diffusivity and thermal diffusivity.

Origin and History

The concept of kinematic viscosity was developed in fluid mechanics to separate a fluid's resistance to shear (dynamic viscosity) from the inertial effect of its density. The SI adopted the coherent unit m²/s as part of the metre-kilogram-second framework, replacing the older CGS stokes (cm²/s).

Law and Notable Facts

The m²/s is the SI-preferred unit, but it is inconveniently large for most liquids, so the millimetre-squared per second (mm²/s), equal to the centistokes, dominates practical tabulation. The Reynolds number, $Re = vL/\nu$, uses kinematic viscosity $\nu$ directly in m²/s.

Real-World Examples and Conversions

Water at 20 °C has a kinematic viscosity of about $1.004\times10^{-6}\ \text{m}^2/\text{s}$ (1.004 cSt). Air at 20 °C is roughly $1.5\times10^{-5}\ \text{m}^2/\text{s}$, higher than water because of air's low density. One $\text{m}^2/\text{s}$ equals $10{,}000\ \text{stokes}$ or $10⁶\ \text{mm}^2/\text{s}$.

What is the square foot per second?

The square foot per second is an imperial and US customary unit of kinematic viscosity, expressing how quickly momentum diffuses through a fluid relative to its density. It appears in older engineering references and in fields where imperial units persist, such as parts of the oil and gas industry.

Definition

One square foot per second is the kinematic viscosity of a fluid in which an area of one square foot's worth of momentum diffusion occurs each second. Because one foot equals exactly 0.3048 metre, the conversion follows directly from squaring that length.

$$1\ \text{ft}^2/\text{s} = 0.0929030\ \text{m}^2/\text{s}$$

Exactly, $1\ \text{ft}^2/\text{s} = (0.3048)^2\ \text{m}^2/\text{s} = 0.09290304\ \text{m}^2/\text{s} = 92903.04\ \text{cSt}$.

Origin and History

The unit derives from the imperial foot, a length whose modern definition was internationally standardized in 1959 as exactly 0.3048 metre. Kinematic viscosity expressed in ft²/s follows the same dimensional pattern as its SI counterpart (m²/s), simply substituting the foot for the metre.

Law and Notable Facts

The square foot per second is a coherent unit within the foot–pound–second system rather than an SI unit. It is a comparatively large unit: even highly viscous industrial fluids rarely exceed a small fraction of 1 ft²/s, so most practical values are much less than one.

Real-World Examples and Conversions

• Water at 20 °C (~1.004 cSt) is only about $1.08 \times 10⁻⁵\ \text{ft}^2/\text{s}$.
• A heavy oil at 100 cSt equals about $1.076 \times 10⁻³\ \text{ft}^2/\text{s}$.
• $1\ \text{ft}^2/\text{s} = 0.09290304\ \text{m}^2/\text{s}$.
• $1\ \text{m}^2/\text{s} \approx 10.7639\ \text{ft}^2/\text{s}$.